Low frequency signal generator



P. E. GRANDMONT LOW FREQUENCY SIGNAL GENERATOR Sept. 9, 1958 Filed Jan. 8, 1954 I I 1/8 h TIM T 1NVENTOR PAUL E. ERANDMEINT I I BYW H 15 ATTORNEY LGW FREQUENQY SEGNAL GENERATOR Paul E. @randrnont, Bioorniield, N. 1., assignor to Curtiss- Wright Corporation, a corporation of Delaware Application .l'anuaiy 3, 1954, Serial No. 402,862

16 Claims. (Cl. 259-36) My invention relates to low frequency generating systems and has particular reference to a novel and improved system for generating test signals having frequencies of low magnitude suitable for testing servo mechanisms, various forms of automatic control systems and low freguelrgcy amplifiers using large amounts of negative feed- In the testing of servo mechanisms, many forms of automatic control systems and low frequency amplifiers having large amounts of negative feed-back, the need arises for signals of low frequency as for example from less than .10 cycle per second to cycles per second, and means for generating such signal-s have been devised. As indicated in the article by l. N. Cage on page 337 of the proceedings of the National Electronics Conference for 1944, use has been made of pairs of Wires rotating at a controlled speed in an electrolytic solution between two charged plates for generating such signals. This, however, is a rather cumbersome device for general use. More frequently variable speed devices have been used to rotate synchro-generators with the resultant low frequency modulated carrier passed through a suitable de-modulator to remove the carrier and leave only the desired low frequency. Such a scheme is described in the article by G. M. Auttura, pages 85 and 86 of the proceedings of the NationalElectronics Conference of 1948. This, however, is again a somewhat complicated and costly scheme. Sinusoidal function potentiometers driven by controlled speed drives have been used but contact difficulties limit them to the lowest frequencies only as for example 10 cycles per second or less and again the cost is high. Electronic resistance-capacitance oscillators have also been devised to directly generate low frequencies, but their low frequency performance is limited and commercial units are costly.

It is accordingly a prime object of my invention to provide a low frequency generating system capable of generating signals over a wide range of test frequencies including very low frequnecies of the order of .10 of a cycle and of providing such a system which can be cheaply assembled from devices current in the present electronic art without the necessity for very low frequency oscillators or mechanical drives.

It is another object of my invention to provide electronic circuitry for generating low frequency test signals having as inputs thereto two signals of which at least one may be varied in frequency and having an output test signal the frequency of which is determined by the difference in frequency between the two input signal-s.

Referring to the drawings, Fig. 1 is a diagrammatic illustration of a low frequency generating system designed to function in accordance with the inventive concept. Fig. 2 is a diagrammatic illustration showing the application of the circuitry of Fig. 1 to the testing of a servo mechanism. Fig. 3 is a diagrammatic illustration showing a modified circuit arrangement for generating low frequency signals in accordance with my invention.

Reference character 1 is intended to designate an l 'atented Sept. 9, 1958 oscillator of the standard laboratory type capable of generating a signal voltage over a frequency range of perhaps 20 cycles as for example between 60 and cycles per second. A transformer 2 has its primary winding 3 connected to the oscillator 1 so that the generated signal is impressed upon such primary winding. As shown the transformer 2 has opposite ends 4a and 4b of its secondary winding 4 connected to the anodes of a pair of diodes 5 and 6 respectively and has a center tap 7 which is connected to one end of a secondary winding 8 of a transformer 9. The other end 8a of the secondary winding 8 is connected through a resistor 10 to the cathode of diode.

5 as at 10a and through another resistor 11 to the cathode of diode 6. Transformer 9 has its primary winding 12 connected to the usually available constant-frequency 60 cycle source of supply, the supply voltage being indicated by reference E. The cathode of diode 5 c nnects at 10a with output terminal 13 of the circuit and the cathode of diode 6 is connected to ground, suitable low-pass filter means, however, being interposed in the circuit for eliminating ripple frequencies in the output signal. Such low-pass filter means, as shown includes the condensers 114, 115, and 116, inductances 117 and 118 with inductance 117 having a condenser 119 in parallel therewith, and resistors 120 and 121. It is to be noted that there is a direct current path from the cathode of diode 5 to output terminal 13, so that the low-pass filter means passes currents over a band of frequencies ranging from O to, for example, 20 cycles per second with substantially constant amplitude response, and yet attenuates ripple frequencies of the order of 60 cycles, for example. The ripple even apart from the low-pass filter means is low, owing to the balanced rectifying circuits as will be more fully explained hereinafter. It is also to be noted that the two rectifying circuits comprising diode 5 and resistor 10, and diode 6 and resistor 11 do not include any charging capacitors. Said circuits therefore provide average rectification rather than peak rectification.

Average half-wave rectification results in a reduction of output amplitude by a factor of approximately as compared to peak half-wave rectification and also in greater ripple. Nevertheless, omission of charging capacitors confers the advantage of a substantially constant amplitude output over the desired pass-band of from 0 to, for example, 20 cycles per second. Also, the wellknown effects of clipping of the rectified output in peak rectifying devices are avoided by resort to average rectification and a sinusoidal output having relatively low distortion is obtained thereby.

In operating thelow frequency generating system the oscillator 1 is operated to generate a signal at some frequency according to the frequency desired for the output test signal. As will be shown the frequency of the output signal is determined by the diiference in frequencies between the input signal to the primary winding 12 of trans former 9 and the frequency of the signal generated by the oscillator 1. The frequency of the input signal to winding 12 is substantially constant at 60 cycles per sec-.

.. ing 12 of transformer 9. Diodes 5 and 6 conduct concurrently over positive half cycles and voltages of substanj 2,851,601 h p a tially equal magnitude at any instant are developed at ground with respect to junction 8a and at junction 10a with respect to junction 8a. The net voltage across resistors 10 and 11 thus is zero at any instant, provided the balance is perfect. Thus the low-pass filter means need attenuate but small unbalance voltages of ripple and therefore can be constructed rather simply and inexpensively. The D. C. components are also substantially cancelled, obviating the need for blocking condensers or transformers, the use of which, of course, would be impractical at frequencies of the order of 0.1 cycle per second.

Assume for a second example that the voltage across winding 8 is maintained at the same value as in the preceding first example, but that oscillator 1 is now energized so as to develop. voltages of frequency differing from the supply frequency and that the voltages developed across the windings of the secondary 4 are equal in magnitude but opposite in phase to one another and moreover have a peak value which is relatively small compared to the peak value of the supply voltage across winding 8. Let the voltage at point 7 with respect to point 8:: be represented by E, cos w t the voltage at point 4a with respect to point 7 be E cos (wt-H?) and the voltage at point 4b with respect to point 7 E,, cos (wt-F) to is the radian frequency equal to 211-71,, f being the supply frequency (usually 60 cycles per second), and w is the radian frequency equal to 211-1, f being the frequency generated by oscillator 1. Let to be greater than w by a difference radian frequency al equal to 21rf f being the difference frequency it is desired to generate. As will be apparent from the discussion hereinafter, the operation of the circuit will be substantially the same if conversely to were greater than a) by the radian frequency al The two last-named voltages appearing across the secondary windings of transformer 2 can be represented as E;- COS and E, cos (w t+w t+0) respectively.

By hypothesis E is relatively large compared to E, and in fact so large, that introduction of the two voltages E substantially does not affect the time positions of the beginning and end of conduction periods of the diodes 5 and 6 or of the crest of the wave or the sinusoidal wave shape of the voltage E as compared to the corresponding time positions and wave shape in the first example, but merely modifies the instantaneous values of the wave E Disregarding the independent contribution of the rectifying circuit energized by -E, for the time being, the voltage at point 4a with respect to point 8a is 7 At the times (n being any integer including zero), this expression reduces to E -f-E cos (w t+0) which is the peak value of the composite wave. This peak value has a constant term B and a sinusoidal term E cos. (w t+ 0) which varies according to the desired difference frequency -f Subject to the assumption that the only effect of the voltage E is in the amplitude variation of the wave E which assumption is valid provided E is large compared to E the average value of the half wave rectified volt age appearing across resistor 10 at point 10a with respect to point So is Of course, there also appear across resistor 10 components of voltage of frequency f and harmonics thereof but these may be filtered out by means of the low-pass filter. Thus the voltage derived from terminal 13 contains a D. C. term and a sinusoidal term varying at the frequency f proportional to E and E, respectively. It is apparent that the apparatus could be operated with but a single secondary winding for transformer 2 and but a single diode 5 with the junction 8a grounded directly, resistor 11 and diode 6 being omitted. But it is also apparent that circuit operation would require rather elaborate low-pass filter means to eliminate the ripple frequencies and would also result'in D. C. component in the output.

Considering now the contribution of the other rectifying circuit energized by the voltage E by a series of steps analogous to the steps in the preceding paragraph there is obtained for the voltage applied at point 4b with respect to point 8::

E, cos W tE,, cos w t cos t-M) +75, sin w t sin (w t-H?) for its value at the times The average net voltage across resistors 10 and Ill at point 10a with respect to ground is HZL FE, cos (w t+0)E,[-E, cos uman}:

E, (cos mH-H) 71' Thus it is seen that by use of the balanced circuit as shown in Fig. 1 there is derived an output proportional to E (cos w t-l-ri) at the desired difference frequency f which is substantially free from any D. C. component. It can be shown that the balanced circuit also tends to cancel even-numbered harmonic voltages of the difference frequency f as may be generated for example by non-linear diode characteristics. Further the balanced circuit also substantially cancels out ripple frequency components in view of the concurring conduction of diodes 5 and 6 as pointed out hereinabove.

There are two other possible modes of operation of the circuit shown in Fig. 1 in addition to the one discussed hereinabove. In the first of said other modes the voltages E are relativelylarge compared to the voltage E,, whereas in the second these voltages are of comparable magnitudes. For the case in which the voltages E are large compared to the E the following considerations govern. For a third example, let the voltage at point 4a with respect to point 7 be represented by E cos wt the voltage at point 4b with respect to point 7 by E,, cos (wt-Hr) 5 and the voltage at point 7 with respect to point Set by E, cos (w t-) As a matter of convenience the time or phase reference in the third example is chosen with respect to the voltage E rather than the voltage E as in the preceding examples. The last-named voltage can be represented by E, COS (wt-w t) which upon expansion becomes E cos wt cos (w t+) |E sin wt sin (w t+) The voltage at point 4a with respect to point 8a is therefore E cos wt-l-E cos wt cos (w t+) +E,. sin wt sin (-w t+ whereas the voltage from point 4b to point 8a is E,, cos (wi|1r)+E, cos wt cos (w t+) +E sin wt Sin (w z+) Subject to assumptions analogous to the assumptions stated for the second example, the voltage at point Mia with respect to point 3a will have a peak value v+ r cos l 'i'q which results in an average rectified voltage of Thus a sinusoidal voltage varying at the desired frequency f is generated and a D. C, term is generated as well. correspondingly the peaks of the voltage at ground with respect to 8a are given by the expression and the net average voltage at point 16a with respect "to ground is therefore simply Again the D. C. component has been cancelled out, but it is apparent that the ripple frequency components are not cancelled out in view of the fact that the diodes 5 and 6 conduct during alternate half cycle periods. Therefore a voltage represented by E cos wt appears at point lila with respect to ground, resulting in a very high ripple.

For the last possible mode of operation wherein the voltages E and E are of comparable magnitudes, it can be shown that a voltage varying at the frequency at f can also be derived. However the simplifying assumptions made in the case of the second and third examples are no longer valid, and therefore the positions in the cycle of the beginning and end of the conduction periods of the diodes 5 and 6 will vary appreciably from cycle to cycle, the wave shape of the composite voltages will be materially altered and may have appreciable kinks and dips, and the position in the cycle of the crest of said waves may be materially shifted from cycle to cycle. As a result the wave shape of the average output at frequency f may be seriously distorted.

It will be obvious at this point that an alternate circuit arrangement to that shown is possible wherein the primary winding 3 rather than winding 12 is supplied with a signal having a substantially constant frequency f being con-' nected for example to an available 60 cycle source, and primary winding 12 is connected to an oscillator for supplying a signal of frequency selected according to the desired output frequency. Such input signals would be summed in the same manner as indicated hereinbe fore and the frequency of the output would be determined as before, by the difference in frequencies f and f An application of the low frequency generator system of Fig. 1 to the testing of a servornechanism is shown in Fig. 2 wherein the filter means comprising the elements 114 through 120 inclusive are shown diagrammatically and indicated by the reference character 18. Output terminal 13 is connected as shown through a resistor 19 to a servo amplifier 20 at its input terminal 21 to supply the input signal to the servo mechanism unit. A D. C. servo motor 22 is connected with the amplifier and operates a slider contact 23 of potentiometer 24 in accordance with the amplifier output. As shown the potentiometer is supplied at opposite ends with positive and negative supply voltages +15 and B respectively, and is grounded at the midpoint thereof. Slider contact 23 is connected by a feed-back line 25 through resistor 26 to input terminal 21 to supply a feed-back voltage to the amplifier in accordance with the position of the slider contact 23 on one side or the other of the grounded midpoint of the potentiometer. The slider contact 23 is positioned according to the magnitude of the alternating output voltage of the low frequency generating system at output terminal 13 first to one side of the grounded midpoint of the potentiometer 24 and then to the other side and movement of the slider contacts is determined by the frequency of the output signal which as previously indicated is dependent upon the frequencies of the two input signals to the low frequency generator system. Movement of the slider contact 23 does not, however, follow the output signal of the generator at all frequencies and it is the purpose of a test set-up such as indicated to determine the relationship between the input signal to a servo mechanism and the movement of the slider contact 23 at various frequencies from the very low frequencies to progressively higher frequencies of the input signal. vin general the movement of the slider contact and the input signal remain substantially in phase at the lower frequencies but tend to get out of phase as the frequency of the input signal increases. As shown an oscilloscope 27 may be provided to compare the input signal with the derived voltage at potentiometer 24 as determined by movement of the slider contact 23 so that the phase relationship between the input and output of the servo mechanism can be ascertained. Oscilloscope 27 is connected to terminal 13 and to slider contact 23 in the manner indicated, for this purpose. The low frequency generating system serves to provide signals over the frequency range required for test purposes includ ing the very low frequencies as for example a .10 of a cycle which as previously indicated is accomplished by supplying the system with input voltages having frequencies which differ in magnitude by an amount substantially corresponding to the desired frequency for the test signal.

Fig. 3 shows a modified form of my invention using full wave rectifying means rather than the half Wave rectifying means indicated for the system hcreinbefore described. in this form of my invention 1 provide an oscillator 28 such as previously described for generating one input signal to the system at variable frequencies which oscillator energizes the primary 29 of a transformer 30. Transformer 30 has its primary winding 29 linked with two secondary windings and 32, and voltages at the oscillator frequency are impressed thereon. Another transformer 33 has its primary winding 34 con nected to a source of supply which may be the standardsource of supply for the area, for example 60 cycles per second and has its secondary windings 35 and 36 respectivelyconnected to windings 31 and 32 for superimposing voltages at the frequency of the supply to primary winding 34 on the voltages impressed across windings 3i and 32 by transformer 30. As shown, one end 353a of winding 35 is connected to one end 331a of the secondary winding 31 and its other end 35b is connected to a cathode of one of the two diodes 3? and to an anode of one of the two diodes 38. The cathode of the other of the two diodes 37 and the anode of the other of the two diodes 38 are connected to end 31b of winding 31. The pair of diodes 37 has its anodes interconnected and the other pair of diodes 38 has its cathodes connected together.

Thus the pairs of diodes 37 and 38 are placed across the series connected windings 31 and 35 in full-wave bridge rectifier connection. Similarly-one end 36a of winding 36 is connected to one end 32a of winding 32 and its other end 3615 is connected to a cathode of one of the two of diodes 39 and to an anode of one of the two diodes 40. The cathode of the other of the two diodes 39 and the anode of the other of the two diodes 40 are connected to end 32b of winding 32. The pair of diodes 39 has its anodes connected together and the other pair of diodes 40 has its cathodes connected together. Thus the pairs of diodes 39 and 40 are placed across the pairs connected windings 32 and 36 also in full-wave bridge rectifier connection. The pairs of diodes 38 and 4t} which may be considered output tubes of the system are connected through suitable low-pass filter means to the output terminal 41 and ground respectively. As indicated the anodes of the pairs of diodes 37 and 39 are interconnected and are further connected with the cathodes of the pairs of diodes 38 and 40 through similar resistors 42 and 43 respectively, which resistors serve as loads for the aforesaid bridge circuits. Because of the symmetry of one bridge circuit with respect to the other, in this form of my invention either each of the pair of equal voltages derived from windings 35 and 36 may be made relatively large compared to each of the pair of equal voltages derived from windings 31 and 32, or vice-versa. According to the former alternative, windings 35 and 36 are arranged so that the voltage at point 35a with respect to point 35b is equal to and in phase with the voltage from 36a to 36b, whereas the voltage at point 31a with respect to point 31b is equal but of opposite phase to the voltage at point 32a with respect to point 3%; the converse is true for the latter alternative. As in the first form of my invention the rectifying circuits are free from charging capacitors, and coupling to the low-pass filter means is direct. The low-pass filter means provided include condensers 44, 45 and 46, inductances 4'7 and 48 with inductance 47 in parallel with a condenser 49, and resistors 50 and 51. In this form of low frequency generator with the frequency from oscillator 28 selected to exceed that to Winding 34 the lowest frequencies which must be filtered from the output signal are twice the frequency of the input voltage to primary winding 34 of transformer 33, and the filter may be designed to cutoff just below this value. In the first form of my inventions frequencies greater than the frequency of the input signal to primary winding 12 must be eliminated.

Thus in this second form, output signals having frequencies twice as great as those which may be produced in the first form of the invention can be generated. A wider frequency range is thus obtained by this somewhat more elaborate form of circuitry but nevertheless simple and inexpensive design as compared to the prior art.

It will now be apparent that I have provided a system for generating signals in the low frequency range including the very lowest frequencies, that the system is particularly applicable for testing purposes and that the design can be simply constructed from existing electronic equipment with great savings as compared to the methods heretofore provided in the prior art.

It should be understood that this invention is not limited to specific details of construction and arrangement thereof herein illustrated, and that changes and modifications may occur to one skilled in the art without departing from the spirit of the invention.

What is claimed is:

l. A low frequency generating system comprising means for generating an alternating current signal of a predetermined single frequency f and of fixed amplitude, a first transformer including a primary winding energized by said alternating current signal and a pair of secondary windings linked with the primary winding such that equal signals of opposite phase are impressed on the said secondary windings, means for generating an alternating current signal voltage of another predetermined single frequency f and of fixed amplitude, a second transformer including a primary winding energized by said alternating current signal of frequency f and a pair of secondary windings linked with the primary winding, one such secondary winding connected in circuit with one secondary winding of the first transformer and the other such secondary winding connected in circuit with the other secondary winding of the first transformer for superimposing a signal voltage of frequency f on each of the said impressed voltages of frequency f, full-wave rectifying means connected in circuit with one secondary winding of the first transformer and one secondary Winding of the second transformer including two pairs of diodes connected across the said one secondary windings of the first and second transformer with the anodes of one pair of diodes connected together and the cathodes of the other pair of diodes connected together, other full wave rectifying means connected in circuit with the other secondary winding of the first transformer and the other secondary winding of the second transformer to produce a net output voltage as determined by the potential differential between the rectified summed voltages, such other rectifying means including two pairs of diodes connected across the said other secondary windings of the first and second transformer with the anodes of one pair of diodes connected together and the cathodes of the other pair of diodes connected together, and low-pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to and greater than the lower of 2 f and 2 f thereby providing a resulting output voltage having a frequency represented by the difference between said frequencies f and f 2. A low frequency generating system for the generation of frequencies of from a fraction of one cycle per second to approximately twenty cycles per second, com prising means for generating an alternating voltage of one predetermined single frequency f and of fixed amplitude, means for superimposing an alternating voltage of another predetermined single frequency and of fixed amplitude on said first-named voltage, means for rectifying the resulting summed voltage, and low-pass filter means connected through direct current means to said rectifying means for filtering said rectified voltage of ripple frequencies thereby to provide a resulting output voltage having a frequency represented by the difference between the frequencies f and f 3. A low frequency generating system for the generation of sinusoidal voltages in a band ranging from a fraction of one cycle per second to approximately twenty cycles per second with substantially constant amplitude over said band and low distortion, comprising means for generating a signal voltage of one predetermined single frequency f and of fixed amplitude, means for superimposing an alternating current voltage of another single predetermined frequency i and of fixed amplitude on said first-named voltage, rectifying means for performing average rectification of the resulting summed voltage, and low-pass filter means connected through direct current means to said rectifying means for filtering said rectified voltage of ripple frequencies to provide a resulting output voltage having a frequency represented by the difference between the frequencies ;f and f 4. A low frequency generating system for the generation of frequencies from a fraction of one cycle per second to approximately twenty cycles per second, comprising means for generating an alternating voltage of a predetermined single frequency f and of fixed amplitude, a first transformer including a primary winding energized by said alternating voltage and a secondary winding linked therewith, means for generating an alternating voltage of another pre-determined single frequency f and of fixed amplitude, a second transformer including a primary winding energized by said voltage of frequency t and a secondary winding linked with the primary winding and connected in circuit with the second winding of the first transformer for superimposing a voltage of frequency f on the voltage of frequency f, means for rectifying the resulting summed voltage to obtain an output voltage, and low-pass filter means connected through direct current means to said rectifying means for filtering said output voltage of frequencies equal to and greater than the lower of f and f thereby providing a resulting output voltage having a frequency represented by the difference between said frequencies f and f 5. A low frequency generating system for the generation of sinusoidal voltages over a band of frequencies ranging from a fraction of one cycle per second to approximately twenty cycles per second with substantially constant amplitude over said band, comprising means for generating an alternating voltage of a pro-determined single frequency f and of fixed amplitude, a first trans former including a primary winding energized by said alternating voltage and a secondary winding linked therewith, means for generating an alternating voltage of another predetermined single frequency f and of fixed amplitude, a second transformer including a primary winding energized by said voltage of frequency f and a secondary winding linked with the primary winding and connected in circuit with the secondary winding of the first transformer for superimposing a voltage of frequency f voltage on frequency 7'', means for performing average rectification of the resulting summed voltage to obtain an output voltage, and low-pass filter means connected through direct current means to said rectifying means for filtering said output voltage of frequencies equal to and greater than the lower of f and f thereby providing a resulting output voltage having a frequency represented by the difference between said frequencies f and f 6. A low frequency generating system for the generation of sinusoidal voltages over a frequency band ranging from a fraction of 1 cycle per second to approximately twenty cycles per second with substantially constant amplitude over said band and low distortion, comprising means for generating a pair of alternating voltages of a predetermined single frequency f and of fixed amplitude, means for superimposing an alternating voltage of another predetermined single frequency 7' and of fixed amplitude on each of the voltages of frequency f to obtain a pair of resulting summed voltages, half wave rectifying means for performing average rectification of one of the resulting summed voltages and other half wave rectifying means for performing average rectification of the other of the resulting summed voltages to obtain a net output voltage as determined by the potential difference between the rectified resulting summed signals, and lowpass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to'and greater than the lower of fand f thereby providing a resulting output voltage having a frequency substantially equal to the difference between the frequency f and f 7. A low frequency generating system for the generation of sinusoidal voltages over a frequency band ranging from a fraction of one cycle per second to approximately twenty cycles per second with substantially constant amplitude over said band and low distortion, comprising means for generating an alternating voltage of a predetermined single frequency f and of fixed amplitude, at first transformer including a primary winding energized by said alternating voltage and a secondary Winding having a center tap and linked with said primary winding such that equal voltage signals of opposite phase are impressed between said center tap and opposite ends of the secondary winding, means for generating an alternating voltage of another predetermined single frequency i and of fixed amplitude, a second transformer including a primary winding energized by said alternating voltage of frequency f and a secondary winding linked with the primary winding and connected in circuit with the secondary winding of thefirst transformer for superimposing a voltage of frequency i on said impressed voltages, half-wave rectifying means connected in circuit with opposite ends of the secondary winding of the first transformer for performing average rectification of the summed voltages to produce a net output voltage as determined by the potential difference between the rectified summed voltages, and low-pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to and greater than the lower of f and f thereby providing a resulting output voltage having a frequency represented by the difference between said frequencies f and f 8. A low frequency generating system for the generation of sinusoidal voltages in a frequency band ranging from a fraction of one cycle per second to approximately twenty cycles per second with' substantially constant amplitude over said band and low distortion, comprising means for generating a pair of alternating signal voltages of a predetermined single frequency f and of fixed amplitude, means for superimposing an alternating voltage of another predetermined single frequency f and of fixed amplitude on each of the alternating voltages of frequency f to obtain a pair of resulting summed voltages, full wave rectifying means for performing average rectification of one of the resulting summed voltages, and other full wave rectifying means for performing average rectification of the other of the resulting summed voltages to obtain a net output voltage as determined by the potential difference between the resulting rectified summed voltage signals, and low pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to and greater than the lower of 2 and 2 thereby providing a resulting output voltage having a frequency substantially corresponding to the difference between the frequencies f and f 9. A low frequency generating system comprising means for generating an alternating current signal of a predetermined single frequency f and of fixed amplitude, a first transformer including a primary winding energized by said alternating current signal and a pair of secondary windings linked with the primary winding such that equal signals of opposite phase are impressed on the said secondary windings, means for generating an alternating current signal voltage of another predetermined single frequency f and of fixed amplitude, a second transformer including a primary winding energized by said alternating current signal of frequency f and a pair of secondary windings linked with the primary winding, one such secondary winding connected in circuit with one secondary winding of the first transformer and the other such secondary winding connected in circuit with the other secondary winding of the first transformer for superimposing a signal voltage of frequency f on each of the said impressed voltages having a frequency 1, full wave rectifying means connected in circuit with the one secondary winding of the first transformer and the one secondary winding of the second transformer, and other full wave rectifying means connected in circuit with the other secondary winding of the first transformer and the other secondary winding of the second transformer for performing average rectification of the summed voltages to produce a net output voltage as determined by the potential differential between the rectified summed voltages, and low-pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to and greater than the lower of 2X1 and 2 fo thereby providing a resulting output voltage having a frequency represented by the difference between said frequencies f and f 10. A low frequency generating system comprising means for generating an alternating current signal of a predetermined single frequency fandof fixed amplitude, a first transformer including a primary winding energized by said alternating current signal and a pair of secondary windings linked with the primary winding such that equal signals of opposite phase are impressed on the said secondary windings, means for generating an alternating current signal voltage of another predetermined single frequency f and of fixed amplitude, a second transformer including a primary winding energized by said alternating current signal of frequency f and a pair of secondary windings linked with the primary Winding, one such secondary winding connected in circuit with one secondary winding of the first transformer and the other such sec ondary winding connected in circuit with the other secondary winding of the first transformer for superimposing a signal voltage of frequency f on each of the said impressed voltages of frequency f, full-wave avearge rectifying means connected in circuit with one secondary winding of the first transformer and one secondary winding of the second transformer including two pairs of diodes connected across the said one secondary windings of the first and second transformer with the anodes of one pair of diodes connected together and the cathodes of the other pair of diodes connected together, other full wave average rectifying means connected in circuit with the other secondary winding of the first transformer and the other secondary winding of the second transformer to produce a net average rectified output voltage as determined by the potential differential between the rectified summed voltages, such other rectifying means including two pairs of diodes connected across the said other secondary windings of the first and second transformer with the anodes ofone pair of diodes connected together and the cathodes of the other pair of diodes connected together, and lowpass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to' and greater than the lower of 2 f and 2 f thereby providing a resulting output voltage having a frequency represented by the difference between said frequencies f and f 11. A low frequency generating system for the generation of frequencies of from a fraction of one cycle per second to approximately twenty cycles per second, comprising means for generating a pair of alternating current signal voltages of one predetermined single frequency f and of fixed amplitude, means for super-imposing an alternating current signal voltage of another predetermined single frequency f and of fixed amplitude on each of the alternating current signal voltages of frequency 1, means for rectifying the resulting summed voltages to obtain a net output voltage including ripple frequencies as determined by the potential difference between the rectified resulting summed voltage signals, and low-pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of ripple frequencies to provide a resulting output voltage having a frequency represented by the difference between the frequencies f and f 12. A low frequency generating system for the generation of sinusoidal voltages over a frequency band ranging from a fraction of one cycle per second to approximately twenty cycles per second with substantially constant amplitude over said band and low distortion, comprising means for generating a pair of alternating current signal voltages having a predetermined single frequency f and fixed amplitudes, means for superimposing an alternating current signal voltage of another single frequency f and of fixed amplitudes on each of the alternating current signal voltages of frequency f, rectifying means for performing average rectification of the summed voltages, means connecting the rectified voltages in opposition to obtain anet output voltage including ripple frequencies,

"12 and low-pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of ripple frequencies to obtain a resulting output voltage having a frequency substantially corresponding to the difference between the frequencies f and f 13. A low frequency generating system for the generation of voltages over a frequency band ranging from a fraction of one cycle per second to approximately twenty cycles per second, comprising means for generating a pair of alternating current signal voltages of a predetermined single frequency f and of fixed amplitude, means for super-imposing an alternating current signal voltage of another single predetermined frequency i and of fixed amplitude on each of the alternating current signalvoltages of frequency f to obtain a pair of resulting summed voltages, half-wave rectifying means for rectifying one of the resulting summed voltages and other half-wave rectifying means for rectifying the other of the resulting summed voltages to obtain a net output voltage as determined "by the potential difference between the rectified resulting summed voltage signals, and low-pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to and greater than the lower of f and f thereby providing a resulting output voltage having a frequency substantially equal to the difference between the frequencies f and f 14. A low frequency generating system for the generation of frequencies of from a fraction of one cycle per second to approximately twenty cycles per second, comprising means for generating a pair of alternating current signal voltages of a predetermined single frequency f and of fixed amplitudes, means for super-imposing an alternating current signal voltage of another predetermined single frequency i and of fixed amplitude on each of the alternating current signal voltages of frequency f to obtain a pair of resulting summed voltages, full-wave rectifying means for rectifying one of the resulting summed voltages, and other full-wave rectifying means for rectifying the other of the resulting summed voltages to obtain a net output voltage as determined by the potential difference between the rectified resulting summed voltage signals, and low-pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to and greater than the lower of 2 and 2]}, thereby providing a resulting output voltage having a frequency substantially corresponding to the difference between the frequencies f and f 15. A low frequency generating system for the generation of voltages over a frequency band ranging from a fraction of one cycle per second to approximately twenty cycles per second, comprising means for generating an alternating current signal voltage of a predetermined single frequency f and of fixed amplitude, a first transformer including a primary winding energized by said alternating current signal and a secondary winding having a center tap and linked with said primary winding such that equal voltage signals of opposite phase are impressed between said center tap and opposite ends of the secondary winding, means for generating an alternating current signal voltage of another predetermined single frequency f and of fixed amplitude, a second transformer including a primary winding energized by said alternating current signal of frequency f and a secondary winding linked with the primary winding and connected in circuit with the secondary winding of the first transformer for superimposing a signal voltage of frequency f on said impressed voltages, half wave rectifying means connected in circuit with opposite ends of the secondary winding of the first transformer for rectifying the summed voltages to produce a net output voltage as determined by the potential differential between the rectified summed voltages, and low-pass filter means connected through direct current means to said rectifying means for filtering said net output voltage of frequencies equal to and greater than the lower of f and f thereby providing a resulting output voltage having a frequency represented by the difference between said frequencies f and f 16. A low frequency generating system comprising means for generating an alternating current signal of a predetermined single frequency f and of fixed amplitude, a first transformer including a primary winding energized by said alternating current signal and a pair of secondary windings linked with the primary winding such that equal signals of opposite phase are impressed on the said secondary windings, means for generating an alternating current signal voltage of another single predetermined frequency f and of fixed amplitude, a second transformer including a primary winding energized by said alternating current signal of frequency f and a pair of secondary windings linked with the primary Winding, one such secondary winding connected in circuit with one secondary winding of the first transformer and the other such secondary winding connected in circuit with the other secondary Winding of the first transformer for superimposing a signal voltage of frequency f on each of the said impressed voltages having a frequency f, full wave rectifying means connected in circuit with the one secondary winding of the first transformer and the one secondary winding of the second transformer, and other full wave rectifying means connected in circuit with the other secondary winding of the first transformer and the other secondary winding of the second transformer for References Cited in the file of this patent UNITED STATES PATENTS 1,684,445 Honaman Sept. 18, 1928 1,794,847 Green Mar. 3, 1931 1,827,843 Green Oct. 20, 1931 2,505,642 Hugenholtz et a1 Apr. 25, 1950 2,676,304 Ensink et a1. Apr. 20, 1954 2,677,054 Cohen Apr. 27, 1954 2,719,940 West Oct, 4, 1955 2,785,306 Johnson et al Mar. 12, 1957 

